Semi- and nonparametric ARCH processes.
Seven Proofs for the Subadditivity of Expected Shortfall
Subadditivity is the key property which distinguishes the popular risk measures Value-at-Risk and Expected Shortfall (ES). In this paper we offer seven proofs of the subadditivity of ES, some found in the literature and some not. One of the main objectives of this paper is to provide a general guideline for instructors to teach the subadditivity of ES in a course. We discuss the merits and suggest appropriate contexts for each proof.With different proofs, different important properties of ES are...
Some applications of time series models to financial data
Some short elements on hedging credit derivatives
In practice, it is well known that hedging a derivative instrument can never be perfect. In the case of credit derivatives (e.g. synthetic CDO tranche products), a trader will have to face some specific difficulties. The first one is the inconsistence between most of the existing pricing models, where the risk is the occurrence of defaults, and the real hedging strategy, where the trader will protect his portfolio against small CDS spread movements. The second one, which is the main subject of...